Equations that changed the world - photo

[Altair]

Equations that changed the world.




Previously:

Einstein explaining his famous formula e=mc2 - GIF
1960s NASA before PowerPoint and using ladders to do math - photos
Hyperboloid of revolution
Chaos theory demonstration - GIF
Richard Feynman explains: What keeps a train on the track?

[mklotz]

Forgot a very important one, Euler's formula...

e^ix = cos x + i sin x

which, when evaluated for x = π, yields the amazing relation...

e^iπ + 1 = 0

An irrational number raised to an irrational, imaginary value yields an integer - astounding.

And here's one way to prove it...

[Toolmaker51]

Forgot a very important one, Euler's formula...

That's because Euler didn't have a good publicist or agent;
or
the convening board felt a third revolutionary concept per mathematician an excess.

[2wheelcharlie]

the chemists secrets are freely told to the carpenter ( emerson)

[Toolmaker51]

the chemists secrets are freely told to the carpenter (emerson)

Note those who needing an exclusive vocabulary to restrain such occurrence.

[mwmkravchenko]

Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )

[mklotz]

Leibnitz independently founded calculus. And there was even a Precursor to Fourier. With even a derivation of the FFT. ( I watched this on YouTube. My Math skills are there on the far back recesses of my shelf of clapping brain cells, rusty and get lubricated only when required )

Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

[mwmkravchenko]

Leibniz (note spelling, Leibnitz is a city in Austria) is responsible for the notation we still use in calculus. Our integral sign is the script form of the letter 's' used in those days. As such, it stood for continuous Summation, much as we now use the Greek capital sigma for discrete summations.

This picture shows this form of the letter as used in the mid 1700s; other examples can be seen in Washington's diaries preserved at Mount Vernon.

Yup, my spelling prowess is slipping little by little. Funny how language changes, is Old English they even used similar spelling to German. Roots of English being German and French for a great part, and a lot of Greek too. Pays to do a little appreciating of how things we use regularly come to be. It's called history. Some of it is even honest!

[mklotz]

Yup, my spelling prowess is slipping little by little. Funny how language changes, is Old English they even used similar spelling to German. Roots of English being German and French for a great part, and a lot of Greek too. Pays to do a little appreciating of how things we use regularly come to be. It's called history. Some of it is even honest!

I have an eidetic memory; once I've seen a word written, its spelling is locked in my memory. Surprisingly, it works for languages I do not speak. It's a blessing and a curse. When young, I won a lot of spelling bees and my wife says she's never seen me misspell a word (although that may be based on a small sample population of grocery lists). On the curse side, whenever I read something the spelling errors stand out like neon and really slow down my usually fast scanning.

English can be a pitfall for the unsure speller. It has the largest vocabulary in the world...

https://www.lexilab.it/en/profession...all-languages/

and prefers single word adjectives rather than descriptive phrases as used in German and the Romance languages. Furthermore, its many contributors lead to a huge collection of homophones, those nasty words that no spell checker can detect when the wrong one is selected. Most homophones are doublets but there are exceptions...

Rose (flower)

Rose (past tense of Rise)

Rows (plural of row (as in of chairs))

Row's (possessive of row)

Rows (third person present tense of to row (as in a boat))

Roes (collections of fish eggs)

Rhos (plural of the Greek letter rho)

[mwmkravchenko]

I have an eidetic memory; once I've seen a word written, its spelling is locked in my memory. Surprisingly, it works for languages I do not speak. It's a blessing and a curse. When young, I won a lot of spelling bees and my wife says she's never seen me misspell a word (although that may be based on a small sample population of grocery lists). On the curse side, whenever I read something the spelling errors stand out like neon and really slow down my usually fast scanning.

English can be a pitfall for the unsure speller. It has the largest vocabulary in the world...

https://www.lexilab.it/en/profession...all-languages/

and prefers single word adjectives rather than descriptive phrases as used in German and the Romance languages. Furthermore, its many contributors lead to a huge collection of homophones, those nasty words that no spell checker can detect when the wrong one is selected. Most homophones are doublets but there are exceptions...

Rose (flower)

Rose (past tense of Rise)

Rows (plural of row (as in of chairs))

Row's (possessive of row)

Rows (third person present tense of to row (as in a boat))

Roes (collections of fish eggs)

Rhos (plural of the Greek letter rho)

Yep I talk about the craziness of English regularly.

I have similar memory for some things. Music being one of them. I was a championship speller way back. But not as much anymore. And it is truly sad because I correspond daily with friends and clients and use a spell checker. Oh well. My Dad told me don't get old. It sucks! To bad he told me in my late 40's

Mark